Variance changes over time and depends on historical data and previous variances; as a result, it is useful to use a GARCH process to model it. In this paper, we use the notion of Conditional Esscher transform to GARCH models to find the GARCH, EGARCH and GJR risk-neutral models. Subsequently, we apply these three models to obtain option prices for the Stock Exchange of Thailand and compare to the well-known Black-Scholes model. Findings suggest that most of the pricing options under GARCH model are the nearest to the actual prices for SET50 option contracts with both times to maturity of 30 days and 60 days.

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We investigate the derivation of option pricing involving several assets following the Geometric Brownian Motion (GBM). First, we propose some derivations based on the basic ideas of the assets. Next, we consider the trivial case where we have n assets. Finally, we consider different drifts, volatilities and Wiener processes but now from n stochastic assets taking into account a fixed-income.

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